glm.izip: Fit an interpretable Zero-Inflated Poisson Generalized Linear...
In thomas-fung/izipr: Interpretable Zero-Inflated Poisson Models in R

Description Usage Arguments Details Value References Examples

The function glm.izip is used to fit an interpretable zero-inflated Poisson generalized linear model with a log-link.

glm.izip(
  formula,
  data,
  ref.lambda = NULL,
  offset = NULL,
  subset,
  contrasts = NULL,
  na.action
)

`formula`	an object of class 'formula': a symbolic description of the model to be fitted to the mean via log-link.
`data`	an optional data frame containing the variables in the model
`ref.lambda`	the rate of a Poisson distribution that baseline zero-inflated odds based on.
`offset`	this can be used to specify an a priori known component to be included
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`contrasts`	optional lists. See the contrasts.arg of model.matrix.default.
`na.action`	a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

Fit an interpretable zero-inflated Poisson regression using maximum likelihood estimation.

The model is

Y_i ~ ZIP_{ν}(μ_i | λ = λ_{ref}),

where

E(Y_i) = μ_i = exp(x_i^T β),

x_i are some covariates.

ν ≥ 0 is the baseline zero-inflated odds relative to a Poisson with rate λ_{ref}.

A fitted model object of class izip similar to one obtained from glm or glm.nb.

The function summary (i.e., summary.izip) can be used to obtain and print a summary of the results.

The functions plot (i.e., plot.izip) and autoplot can be used to produce a range of diagnostic plots.

The generic assessor functions coef (i.e., coef.izip), logLik (i.e., logLik.izip) fitted (i.e., fitted.izip), nobs (i.e., nobs.izip), AIC (i.e., AIC.izip) and residuals (i.e., residuals.izip) can be used to extract various useful features of the value returned by glm.izip.

An object class 'izip' is a list containing at least the following components:

`coefficients`	a named vector of coefficients
`stderr`	approximate standard errors (using observed rather than expected information) for mean coefficients
`residuals`	the response residuals (i.e., observed-fitted)
`fitted_values`	the fitted mean values
`rank`	the numeric rank of the fitted linear model for mean
`linear_predictors`	the linear fit for mean on log scale
`df_residuals`	the residuals degrees of freedom
`df_null`	the residual degrees of freedom for the null model
`null_deviance`	The deviance for the null model. The null model will include only the intercept.
`deviance; residual_deviance`	The residual deviance of the model
`y`	the `y` vector used.
`X`	the model matrix for mean
`model`	the model frame for regression
`call`	the matched call
`formula`	the formula supplied for regression
`terms`	the `terms` object used for regression
`data`	the `data` argument
`offset`	the `offset` vector used

Huang, A. and Fung, T. (2020). Zero-inflated Poisson exponential families, with applications to time-series modelling of counts.

## article production by graduate students in
## biochemistry PhD programs of Long (1990, 1997)
data(bioChemists)
M_bioChem <- glm.izip(art ~ ., data = bioChemists)
summary(M_bioChem)
plot(M_bioChem) # or autoplot(M_bioChem)

## Root counts for propagated columnar apple shoots of
## Ridout, Hinde & Demetrio (1998).
data(appleshoots)
M_shoots <- glm.izip(roots ~ 1 +
  1 + factor(photo) * factor(bap),
data = appleshoots
)
summary(M_shoots)
plot(M_shoots) # or autoplot(M_bioChem)